Answer:
The standard deviation would stay the same
Explanation:
Given:
Salaries as:
$3,500
$4,000
$4,500
and after $100 raise
$3,600
$4,100
$4,600
The average of the salaries before raise
= ( $3,500 + $4,000 + $4,500 ) / 3 = $4,000
The standard deviation = [tex]\sigma=\sqrt{\frac{(mean-x_i)^2}{n}}[/tex]
and
[tex]\sigma=\sqrt{\frac{(4,000-3500)^2+(4,000-4000)^2+(4,000-4500)^2}{3}}[/tex]
or
[tex]\sigma=\sqrt{\frac{250000+0+250000}{3}}[/tex]
or
[tex]\sigma=408.24[/tex]
and, after the raise
the average = ( $3,600 + $4,100 + $4,600 ) / 3 = $4,100
now,
the standard deviation ,
[tex]\sigma=\sqrt{\frac{(4,100-3600)^2+(4,100-4100)^2+(4,100-4600)^2}{3}}[/tex]
or
[tex]\sigma=\sqrt{\frac{250000+0+250000}{3}}[/tex]
or
[tex]\sigma=408.24[/tex]
therefore, The standard deviation would stay the same
